This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A196504 #26 Feb 11 2025 13:49:50
%S A196504 2,0,2,8,7,5,7,8,3,8,1,1,0,4,3,4,2,2,3,5,7,6,9,7,1,1,2,4,7,3,4,7,1,4,
%T A196504 3,7,6,1,0,8,3,8,0,0,2,8,7,5,9,3,9,4,0,8,8,8,1,7,1,6,6,0,7,4,4,4,9,8,
%U A196504 6,6,5,0,3,1,0,4,2,7,6,2,3,4,5,9,2,2,7,9,5,1,5,0,4,2,5,6,3,0,6,3,9
%N A196504 Decimal expansion of the least x > 0 satisfying x + tan(x) = 0.
%C A196504 Let L be the least x > 0 satisfying x + tan(x) = 0.
%C A196504 Then L is also the least x > 0 satisfying x = (sin(x))(sqrt(1+x^2)).
%C A196504 Consequently, for 0 < x < L, for all p > 0, 1/sqrt(1+x^2) - 1/x^p < sin(x) < 1/sqrt(1+x^2) for 0 < x < L.
%C A196504 See A196500-A196503 and A196505 for related constants and inequalities.
%C A196504 The number L also occurs in connection with Du Bois Reymond's constants; see the Finch reference.
%C A196504 For x = L the area of right triangle with vertices (0,0), (x,0) and (x,sin(x)), i.e., the one inscribed into the half-wave curve, is maximal. - _Roman Witula_, Feb 05 2015
%D A196504 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 239.
%H A196504 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A196504 L = 2.02875783811043422357697112473471437610838002...
%e A196504 1/L = 0.4929124517549075741877801898222329769156970132...
%t A196504 Plot[{Sin[x], x/Sqrt[1 + x^2]}, {x, 0, 9}]
%t A196504 t = x /.FindRoot[Sin[x] == x/Sqrt[1 + x^2], {x, .10, 3}, WorkingPrecision -> 100]
%t A196504 RealDigits[t] (* A196504 *)
%t A196504 1/t
%t A196504 RealDigits[1/t] (* A196505 *)
%o A196504 (PARI) solve(x=2,3, sin(x)-x/sqrt(1+x^2)) \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A196504 Cf. A196505, A196500, A196502.
%K A196504 nonn,cons
%O A196504 1,1
%A A196504 _Clark Kimberling_, Oct 03 2011